Distinguished bases of exceptional modules

Exceptional modules are tree modules. A tree module usually has many tree bases and the corresponding coefficient quivers may look quite differently. The aim of this note is to introduce a class of exceptional modules which have a distinguished tree basis, we call them radiation modules (generalizing an inductive construction considered already by Kinser). For a Dynkin quiver, nearly all indecomposable representations turn out to be radiation modules, the only exception is the maximal indecomposable module in case E_8. Also, the exceptional representation of the generalized Kronecker quivers are given by radiation modules. Consequently, with the help of Schofield induction one can display all the exceptional modules of an arbitrary quiver in a nice way.Comment: This is a revised and slightly expanded version. Propositions 1 and 2 have been corrected, some examples have been inserte

Psychodynamic Perspectives on Relationship: Implications of New Findings From Human Attachment and the Neurosciences for Social Work Education

In this article, the historical significance of the therapeutic relationship in social casework theory and practice is discussed and elaborated on in relation to contemporary psychodynamic theories and constructs, such as the therapeutic alliance, the holding relationship, and selfobject theory. The significant contributions of investigators in such diverse fields as infant attachment, neurobiology, and feminist theory are then discussed in relation to these psychoanalytic ideas. Based in part upon recent research being conducted in such fields, a more central role is proposed for psychodynamic conceptions of relationship in the education of social work clinicians

The double Ringel-Hall algebra on a hereditary abelian finitary length category

In this paper, we study the category $\mathscr{H}^{(\rho)}$ of semi-stable coherent sheaves of a fixed slope $\rho$ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of $\mathscr{H}^{(\rho)}$ and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.Comment: 29 page

Better preparation and training determine home care workers’ self-efficacy in contributing to heart failure self-carebetter preparation

Objective Identify determinants of home care workers’ (HCW) self-efficacy in contributing to heart failure (HF) self-care. Methods Secondary analysis of a survey (n = 328) examining characteristics of HCWs caring for adults with HF in New York. Self-efficacy assessed using Caregiver Self-Efficacy in Contributing to Self-Care Scale. Standardized scores range 0–100; ≥ 70 points indicate adequate self-efficacy. Characteristics determined by self-efficacy (low vs. adequate). Prevalence ratios with 95% confidence intervals (PR [95% CI]) were estimated using multivariable Poisson regression with robust standard errors. Results Home care workers with adequate self-efficacy had at least some prior HF training (55% vs. 17%, p < .001) and greater job satisfaction (90% vs. 77%, p = .003). Significant determinants for adequate self-efficacy were employment length (1.02 [1.00–1.03], p = .027), preparation for caregiving (3.10 [2.42–3.96], p < .001), and HF training (1.48 [1.20–1.84], p < .001). Conclusion Home care agencies and policy-makers can target caregiving preparation and HF training to improve HCWs’ confidence in caring for adult HF patients

Liouville coherent states

For a certain class of open quantum systems there exists a dynamical symmetry which connects different time-evolved density matrices. We show how to use this symmetry for dynamics in the Liouville space with time-dependent parameters. This allows us to introduce a concept of generalized coherent states (e.g. density matrices) in the Liouville space. Dynamics of this class of density matrices is characterized by robustness with respect to any time-dependent perturbations of the couplings. We study their dynamical context while focusing on common physical situations corresponding to compact and non-compact symmetries.Comment: 6 pages, 3 figures, accepted to EP

Exploring complex networks via topological embedding on surfaces

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The local properties of the network are affected by the surface genus which, for example, produces significant changes in the degree distribution and in the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwoveness, changing the scaling properties from large-world-kind (small genus) to small- and ultra-small-world-kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description. Within such a framework, we study the properties of topologically-embedded graphs at high and low `temperatures' observing the formation of increasingly regular structures by cooling the system. We show that the cooling dynamics is strongly affected by the surface genus with the manifestation of a glassy-like freezing transitions occurring when the amount of topological disorder is low.Comment: 18 pages, 7 figure

Molecular basis of RNA polymerase III transcription repression by Maf1

RNA polymerase III (Pol III) transcribes short RNAs required for cell growth. Under stress conditions, the conserved protein Maf1 rapidly represses Pol III transcription. We report the crystal structure of Maf1 and cryo-electron microscopic structures of Pol III, an active Pol III-DNA-RNA complex, and a repressive Pol III-Maf1 complex. Binding of DNA and RNA causes ordering of the Pol III-specific subcomplex C82/34/31 that is required for transcription initiation. Maf1 binds the Pol III clamp and rearranges C82/34/31 at the rim of the active center cleft. This impairs recruitment of Pol III to a complex of promoter DNA with the initiation factors Brf1 and TBP and thus prevents closed complex formation. Maf1 does however not impair binding of a DNA-RNA scaffold and RNA synthesis. These results explain how Maf1 specifically represses transcription initiation from Pol III promoters and indicate that Maf1 also prevents reinitiation by binding Pol III during transcription elongation

LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies

We extend the classical LR characterization of chirotopes of finite planar families of points to chirotopes of finite planar families of pairwise disjoint convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a chirotope of finite planar families of pairwise disjoint convex bodies if and only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the set of 3-subsets of J is a chirotope of finite planar families of pairwise disjoint convex bodies. Our main tool is the polarity map, i.e., the map that assigns to a convex body the set of lines missing its interior, from which we derive the key notion of arrangements of double pseudolines, introduced for the first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio